"Use this Lesson Notes to Quickly Teach Percentages Without Stress"

SUBJECT:  NUMBER THEORY

TOPIC: NUMBER THEORY

LESSON: MEANING OF PERCENTAGE, FINDING PERCENTAGE ON GIVEN PROBLEMS.

PREVIOUS KNOWLEDGE: PUPIL CAN IDENTIFY AND WRITE FRACTIONS, AND DECIMAL NUMBERS AS WELL AS MULTIPLY, DIVIDE,ADD OR SUBTRACT THEM.

 LESSON OBJECTIVES: BY THE END OF THE LESSON, PUPILS WILL BE ABLE TO : WRITE A FRACTION OR DECIMAL NUMBER AS PERCENTAGE, STATE ONE OR MORE SITUATIONS WHERE PERCENTAGE IS USED IN DAILY LIFE, WRITE PERCENTAGES , FIND PERCENTAGE OR RATE IN A GIVEN PROBLEM.

TEACHING METHOD: DEMONSTRATION, GROUP DISCUSSION, ASSIGNMENT METHODS.

DURATION: 45 MINUTES

DATE:

INTRODUCTION

Read each of the following :   1,   5 ,  20 ,    50  . What name is generally given to such numbers?

                                                     2   11   100   100

The numbers above are fractions with different denominators; 2, 11, and 100. We will be more concern with fractions having denominator 100. The fractions with denominator 100 can be written as 20%, 50%. The symbol % is used to represent percent.

The number 20  or 20%  is read as 20 percent ; meaning 20 out of 100. Similarly 50 or 50% is read as 50

                  100                                                                                              100

Percent; meaning  50 out of 100.

PRESENTATION

Definition.  A percent or rate is any fraction in which the denominator is 100. A percentage means out of a hundred or per hundred. Examples   i)   40   or 40%

                                                            100

                                                        ii)   60   or 60%

                                                             100

The symbol % represents the denominator in each of the above percentages. It means that percentage is denoted by the symbol %.

USING PERCENTAGES IN DAILY LIFE

Percentages are used in many ways in everyday life.

  EXAMPLES

i)                    In an election, “ 40% voters turn out” means 40 out of every 100 voters actually voted.

ii)                  In a math test, “ 90% score” means that a pupil scored 90 out of 100 possible points for the test.

WRITING A FRACTION AS A PERCENTAGE.

 It is possible to convert a fraction or decimal number into percentage as shown in the examples below.

Example 1. Express each of the following fractions as percentages: a) 7 ,   b)  5 ,   c) 5  .

                                                                                                         10         8          4

                                  SOLUTION

Method 1.  Make an equivalent fraction with denominator 100 in each of the above, the write the percentage.

a)      7  =  7 ×  10  =  70  = 70%

10    10   10     100

7  =  70%

10

b)      5  =  5 × 12.5 = 62.5 =62.5%

8      8    12.5     100

5 =62.5%

8

c)      5 =  5 × 25 = 125 = 125%

4     4     25    100

5 = 125%

4

Method 2.  Change the fraction into a decimal number the multiply by 100%.

a)       7 =  7   × 100% =  0.7 × 100%= 70%

10    10

b)      5 =   5  ×100%=  .625 × 100% = 62.5%

8      8

c)       5  =   5 × 100% = 1.25× 100% = 125%

4        4

We can calculate percentages in election results, score in an examination, health survey, number of birth in a community, boys or girls in a school and many more. Below are a few exercises on this.

 Example  1.   A pupil scored 17 marks out of 20 in a mathematics test. What percentage does this score represent?

                 Solution

Marks scored = 17

   Total marks = 20

Score as fraction =   17 . (Convert this to percentage).

                                20

As percentage;  17 = 17 ×    5  =  85 = 85%

                         20    20       5      100

 Therefore score of   17 = 85%

                                20

May use method 2 above if you wish.

Example 2.  Out of 64 voters who registered for an election, only 16 actually voted.   a) What percentage does this represent? b) what is the percentage those who did not vote.

                    Solution

a)      Those who voted = 16

              Total who registered = 64

Voters as fraction; 16 = 16× 100% = 0.25×100%

                                  64    64

                                  16 = 25%.

                                  64

b)       Total number of voters= 64

  Number that voted= 16

 Number who did not vote= 64-16=48

 Fraction of those who did not vote=  48

                                                         64

Percentage those who did not vote= 48 ×100% = 75%.

                                                        64

            Percentage of those who did not vote= 100% - percentage of those who voted.

            Percentage of those who do not vote= 100% - 25% = 75%.

You can express one quantity as a percentage of another, but make sure both quantities are in the same unit. To find a percentage change, follow these two steps.

i)                    Subtract to find the change

ii)                  Use the proportion; Percentage required= amount of change × 100%

                                                                 Original amount

Example 3 . 26 cm of wood is cut off a board of 130 cm long. What percentage of the wood remained?

                          Solution

Total length=  130 cm

Length cut off = 26cm

Amount of change= 130cm-26cm =104cm.

Percentage required= amount of Change ×100%

                                  Original amount

Percentage of wood left= 104×100%= 80%.

                                        130

To find the percentage of any number, change the percentage to a fraction and multiply by that number.

Example 4 . What number is 60% of 85?

                           Solution

Let the number be n.

Now, n= 60% of 85 ( of means multiplication).

n = 60% × 85

n = 60  × 85

      100

n= .6 × 85

n= 51

Hence, 60% of 85 is 51.

EVALUATION

1)      Write as percentage  a) 2     b)  6 , c)  1

                                    5          25      50

2)      In a class, 9 out of the 26 students are in the Science club. What percentage of the class is in the science club.

3)      5% of a certain number is 21. What is the number.

4)      A elephants sleeps 15% of the 24 hours in a day. How many hours does the elephant sleep in a day.

5)      In a bag of 200 0ranges, 18 are bad. What percentage is; a) bad? , b) good?

6)      A man bought a dish for 7,000 FRS and sold it for 5,600 FRS. What percentage of his money did he lose?

7)      There are 34 girls in a class of 60 pupils. What percentage of the class are boys.

SUMMARY

>To change a fraction to percentage, convert it to an equivalent fraction with denominator 100 then write new numerator with the symbol attached. Or change the fraction to decimal and multiply it by 100 percent or 100%. See example 1 above.

>To calculate a number in a given percentage, change the percentage to decimal and multiply by the number found in the question. See example 4 above.

>To express one quantity as a given percentage of another, make sure both quantities are in the same unit of measurement then calculate the percentage change as follows:

         Percentage required= amount  of change × 100% , see examples 2 and 3 above.

                                            Original amount

CONCLUSION

1)      A  cake has a mass of  2.5 kg. it contains 0.75kg of fruit. What percentage of fruit is in that cake?

2)      In an exam, a pupil scored 60 marks out of possible 80. What percentage is this?

3)      Three girls a absent from a class of 25 girls. What percentage of the class was absent.

4)      The information  below shows the percentage of the recommended daily allowance (RDA) for some nutrients in a 6 gram of baked potato

NUTRIENTS – magnesium,   iron,      vitamin b₆

         %  RDA -  14%                 34%          35%

a)      Write each percentage as a fraction and as a decimal

b)      Suppose you eat 6g of potato, what percentage of each nutrient do you still need to meet the required daily allowance (RDA).

NB. More  Lessons Notes on percentage alongside exercises coming soon.